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Question
Choose the correct option.
In which of the following systems will the radius of the first orbit of the electron be smallest?
Options
Hydrogen
Singly ionized helium
Deuteron
Tritium
Solution
Singly ionized helium
Explanation:
According to Bhor's theory, the radius of an atomic number z atom's nth orbit is: `r prop "n"^2/"Z"`.
Where n is the orbit number.
(i) For hydrogen,
∴ n = 1 and Z = 1
Therefore, `r prop "n"^2/"Z"`
⇒ r ∝ 1
(ii) For Helium,
∴ n = 1 and Z = 2
Therefore, `r prop "n"^2/"Z"`
`=> "r" prop 1/2`
(iii) For Deuteron.
∴ n = 1 and Z = 1
Therefore, `r prop "n"^2/"Z"`
`=> "r" prop 1`
(iv) For Tritium,
∴ n = 1 and Z = 1
Therefore, `r prop "n"^2/"Z"`
`=> "r" prop 1`
Hence, the smallest is Helium. The correct option is Singly ionized helium.
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